Physics Module for 2014 E.C.ESSLCE Exam

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Questions and Answers

What is the difference between scalars and vectors?

Scalars are physical quantities with only magnitude, while vectors have both magnitude and direction.

How are vectors represented analytically?

Vectors are represented analytically by a letter with an arrow over its head or with bold face letter.

Which method is used to represent vectors by drawing a straight line with an arrow to scale?

Scalar method

Geometrical method (correct)

Algebraic method

Analytical method

Vector addition is not simple algebraic addition, it obeys the laws of vector addition. The resultant of two vectors having the same direction is the ________ of the two vectors.

algebraic sum Signup and view all the answers

How is the direction of the resultant vector determined when two vectors act at right angles to each other?

The direction is determined using trigonometry, typically by finding the arctan of the ratio of the magnitudes of the two vectors. Signup and view all the answers

What are the types of forces according to Chapter Four: Dynamics? (Select all that apply)

Applied force Signup and view all the answers

Angular position, angular velocity, and angular acceleration are topics covered in which chapter?

True Signup and view all the answers

What is the type of motion discussed in Chapter Six?

Oscillatory motion Signup and view all the answers

______ is the law discussed in Chapter Eight related to electric charges.

Coulomb Law Signup and view all the answers

Match the following topics with the correct chapter in the physics module:

Work, energy, and power = Chapter Five Electrostatics and Magnetism = Chapter Eight Electric current and Magnetism = Chapter Nine Electromagnetic Induction and AC current = Chapter Ten Signup and view all the answers

What is the equation representing angular momentum according to Eqn. 3.6?

$L = I\omega$ Signup and view all the answers

What does Eqn. 3.7 represent?

$I_i \omega_i = I_f \omega_f$ Signup and view all the answers

What is the condition for two or more vectors to be equal?

The same physical quantities, have the same magnitude, and have the same direction. Signup and view all the answers

What are the units for the gravitational constant G?

N m² / kg² Signup and view all the answers

What is the formula for calculating the magnitude and direction of the car's resultant displacement?

Magnitude = 39.0 km, Direction = 39.0 degrees west of north. Signup and view all the answers

In dynamics, what are the fundamental concepts that are described by Newton's laws of motion?

All of the above Signup and view all the answers

What are the components of a vector in a three-dimensional space?

Ax î + Ay ĵ + Az k̂ Signup and view all the answers

What is a unit vector and how is it represented?

A dimensionless vector with unit magnitude, represented as Â = A / |A|. Signup and view all the answers

Explain the scalar-vector multiplication and provide one rule associated with it.

Scalar multiplication changes the magnitude but not the direction of a vector. One rule is that multiplying by 1 does not change the vector. Signup and view all the answers

What is the formula for the dot product of two vectors A and B?

A · B = |A||B| cos(θ) Signup and view all the answers

What is the result of the cross product of vector A = (ax î + ay ĵ + az k̂) and vector B = (bx î + by ĵ + bz k̂)?

(ay bz - az by) î + (az bx - ax bz) ĵ + ( ax by - ay bx) k̂ Signup and view all the answers

What is the free-fall acceleration on the planet where an astronaut can jump a maximum horizontal distance of 15.0m with an initial speed of 3.00m/s?

9.81 m/s^2 Signup and view all the answers

What is the term used to describe the acceleration that is always toward the center of a circle, perpendicular to velocity?

Centripetal acceleration Signup and view all the answers

What is the time taken for one complete rotation known as?

Period (T) Signup and view all the answers

What is the unit of angular displacement?

Radian (rad) Signup and view all the answers

How is average angular velocity defined?

Rate of change of the angular displacement of an object with respect to time Signup and view all the answers

What is the equation that describes the relationship for uniformly accelerated angular motion?

ω = ωo + αt Signup and view all the answers

What quantity is expressed as a cross product of distance from the axis of rotation and linear momentum?

Angular momentum (L) Signup and view all the answers

What does the moment of inertia of a body depend on?

Size of the body, shape of the body, point of axis of rotation Signup and view all the answers

Define Torque.

Rotational effect of force; Measure of force that causes an object to rotate around an axis. Signup and view all the answers

What factors does the magnitude of torque depend on?

Size of force, moment arm of force, line of action of force Signup and view all the answers

What is the formula for calculating torque?

τ = F rsin(θ) Signup and view all the answers

An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. How long does the electron take to travel this 1.5 cm?

2.85 x 10^-8 s Signup and view all the answers

An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. What is its acceleration?

1.40 x 10^14 m/s^2 Signup and view all the answers

A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its original velocity?

9.76 m/s Signup and view all the answers

A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its acceleration?

-0.41 m/s^2 Signup and view all the answers

A car traveling at a constant speed of 45m/s passes a trooper hidden behind a billboard. One second after the car passes, the trooper sets out to catch it at an acceleration of 3.0m/s^2. How long does it take for the trooper to overtake the car?

15 s Signup and view all the answers

A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. What is its acceleration?

-31.06 mi/hr^2 Signup and view all the answers

A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. If the jet touches down at position xi = 0, what is the final position of the plane?

140 mi Signup and view all the answers

A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. What is the time interval needed for the jet to come to rest?

20 s Signup and view all the answers

A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. Can this jet land on an airport where the runway is 0.8 km long?

No Signup and view all the answers

What is the mathematical expression of the restoring force dependent on?

Specific physical system Signup and view all the answers

What is the defining property of linear momentum?

Ability to cause change through motion Signup and view all the answers

Linear momentum is the product of mass of the system with its ________.

velocity Signup and view all the answers

Linear momentum is a scalar quantity.

False Signup and view all the answers

What is impulse defined as?

Product of the force acting on an object and the time for which the force acts Signup and view all the answers

Match the following collision types with their descriptions:

Elastic Collision = Collision type where both kinetic energy and momentum are conserved Inelastic Collision = Collision type where only momentum is conserved but kinetic energy is not conserved Perfectly Elastic Collision = Collision type where kinetic energy is fully conserved Perfectly Inelastic Collision = Collision type where colliding objects stick together after collision Signup and view all the answers

Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors?

A ~ could be larger or smaller than AB, depending on the angle between the vectors Signup and view all the answers

Which of the following is equivalent to the scalar product: (A ~ × ~A) • ~B?

(A ~ × ~A) • (B ~ × B) Signup and view all the answers

Which of the following statements is true about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors?

|A ~ × B| is smaller than AB Signup and view all the answers

Is the triple product defined by A • (B × C) a scalar or a vector quantity?

Scalar Signup and view all the answers

What are the directions of (a) A × B and (b) B × A if vector A is in the negative y direction and vector B is in the negative x direction?

(a) -k̂, (b) k̂ Signup and view all the answers

Calculate the M • N, M × N, and the angle between M and N given M = 6î + 2ĵ - k̂ and N = 2î - ĵ - 3k̂.

M • N = 8, M × N = -8î + 18ĵ - 10k̂, Angle between M and N = 98.13 degrees Signup and view all the answers

Study Notes

Vectors

Scalar quantities: physical quantities with only magnitude, e.g., electric charge, density, mass
Vector quantities: physical quantities with both magnitude and direction, e.g., velocity, force, torque, electric field

Vector Representation

Analytical methods: represented by a letter with an arrow over its head or with bold face letter, e.g., →F or F, →P or P, →A or A
Graphical/Geometrical methods: represented by a straight line with an arrow, where length is the magnitude and arrow direction is the direction

Vector Addition and Subtraction

Resultant vector (R): the sum of two or more vectors
Vector subtraction: addition of the negative vector, e.g., →R = →A - →B = →A + (-→B)
Vector addition laws:
- The resultant of two vectors with the same direction is the algebraic sum of the two vectors with the same direction as both.
- Not commutative: order of vectors matters, e.g., →A + →B ≠ →B + →A
- Associative: (→A + →B) + →C = →A + (→B + →C)

Key Concepts

Magnitude: the size or amount of a vector
Direction: the orientation or direction of a vectorHere are the study notes for the text:

Kinematics

Definition: Kinematics is a branch of mechanics that describes the motion of an object without reference to the cause of motion (force).

One or Two Dimensional (2D) Motion

Motion: Continuous change of position with time.
Position: Location of an object with respect to a chosen reference frame or point.
Reference Frame: A system of graduated lines symbolically attached to a body that serves to describe the position of points relative to the body.

Types of Motion

Translational Motion: When all points of an object move the same distance in a given time.
- Rectilinear motion: Object moves in a straight line (e.g. car moving in a straight line, bullet being fired).
- Curvilinear motion: Object moves along a curved path (e.g. child going down a slide, bird flying in the sky).
Rotational Motion: When an object moves about an axis and different parts of it move by different distances in a given interval of time.
- Examples: Blades of a rotating fan, merry-go-round, blades of a windmill.
Vibrational Motion: When a body moves to and fro about its mean position.
- Examples: Pendulums, swings, tuning forks.

Let me know if this meets your requirements!### Vibrational Motion

Vibrational motion can be periodic or non-periodic

Kinematics of the Particle

Motion in 1D

Motion of a particle along a straight line in a fixed direction (or motion along one coordinate axis)
Example: a car moving along a flat straight narrow road

Kinematical Terms

Distance: total path length covered by the moving object
Displacement: change of position (shortest distance between start and end of motion)
Speed: rate of change of distance in a unit time
Average Speed: total distance traveled by the total time required to cover the distance
Velocity: rate of change of displacement as a function of time
Average Velocity: change of displacement divided by the time interval during which the displacement occurs
Instantaneous Velocity: velocity of the particle at a given instant of time (limit of average velocity as Δt approaches to zero)
Instantaneous Speed: magnitude of instantaneous velocity

Acceleration

Acceleration: rate of change of velocity
Average Acceleration: change in velocity divided by the time interval during which the change in velocity occurs
Instantaneous Acceleration: acceleration of the particle at a given instant of time (limit of average acceleration as Δt approaches to zero)

Uniform Motion in 1D

Uniform Motion: equal distances traveled in equal intervals of time
Acceleration: zero
Velocity: remains constant
Speed: equal to the actual speed
Instantaneous Velocity: equal to the actual velocity

Uniformly Accelerated Motion in 1D

Uniformly Accelerated Motion: motion with constant acceleration
Velocity: changes with uniform rate
Equations of Motion:
- v(t) = vi + at
- ∆x = vi t + (1/2) at^2
- v^2 = vi^2 + 2a∆x

Free Falling Bodies

Free Falling Bodies: objects moving freely under the influence of gravity alone
Equations of Motion:
- vy = gt
- ∆y = (1/2) gt^2
- vy^2 = 2g∆y

Two-Dimensional Motion

Two-Dimensional Motion: motion in a plane (two coordinate axes simultaneously)
Displacement: ∆~r = ~rB - ~rA
Average Velocity: ~vav = ∆~r / ∆t
Instantaneous Velocity: v(t) = lim (∆~r / ∆t) as Δt approaches to zero
Average Acceleration: ~aav = ∆~v / ∆t
Instantaneous Acceleration: a(t) = lim (∆~v / ∆t) as Δt approaches to zero

Projectile Motion

Projectile Motion: motion of an object in a plane under the influence of gravity alone
Trajectory: parabolic path
Horizontal Motion: uniform motion (ax = 0)
Vertical Motion: uniformly accelerated motion (ay = -g)
Equations of Motion:
- x(t) = v0x t
- y(t) = v0y t - (1/2) gt^2
- v0y = v0 sinθ
- ymax = v0y^2 / 2g
- t = 2v0y / g
- R = v0^2 sin(2θ) / g

Circular Motion

Circular Motion: motion in a circular path at a constant speed
Uniform Circular Motion: constant speed and direction
Velocity: not constant due to continuous change in direction
Acceleration: radial acceleration (a = v^2 / r)

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Description

This quiz is a part of the Pre-University Remedial Program for the 2014 E.C.ESSLCE exam in Ethiopia, covering the Physics Module, specifically vectors and scalar quantities.